Log in

Relevant bibliographies by topics / Volterra integro-differential equations / Journal articles

To see the other types of publications on this topic, follow the link: Volterra integro-differential equations.

Journal articles on the topic 'Volterra integro-differential equations'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 July 2025

Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles

Select a source type:

Consult the top 50 journal articles for your research on the topic 'Volterra integro-differential equations.'

Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.

You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.

Browse journal articles on a wide variety of disciplines and organise your bibliography correctly.

1

Tarang, M. "STABILITY OF THE SPLINE COLLOCATION METHOD FOR SECOND ORDER VOLTERRA INTEGRO‐DIFFERENTIAL EQUATIONS." Mathematical Modelling and Analysis 9, no. 1 (2004): 79–90. http://dx.doi.org/10.3846/13926292.2004.9637243.

Full text

Abstract:

Numerical stability of the spline collocation method for the 2nd order Volterra integro‐differential equation is investigated and connection between this theory and corresponding theory for the 1st order Volterra integro‐differential equation is established. Results of several numerical tests are presented. Straipsnyje nagrinejamas antros eiles Volteros integro‐diferencialiniu lygčiu splainu kolokaci‐jos metodo skaitinis stabilumas ir nustatytas ryšys tarp šios teorijos ir atitinkamos pirmos eiles Volterra integro‐diferencialiniu lygčiu teorijos. Pateikti keleto skaitiniu eksperimentu rezultat

APA, Harvard, Vancouver, ISO, and other styles

2

Butris, Raad Noori, and Noori R. Noori. "APPROXIMATE AND STABILITY SOLUTION FOR NON-LINEAR SYSTEM OF INTEGRODIFFERENTIAL EQUATIONS OF VOLTERRA TYPE WITH BOUNDARY CONDITIONS." IJISCS (International Journal of Information System and Computer Science) 7, no. 2 (2023): 124. http://dx.doi.org/10.56327/ijiscs.v7i2.1482.

Full text

Abstract:

In this paper, we investigate the approximation and stability solutions of non-linear systems of integro-differential equations of Volterra type with boundary conditions, by using the numerical-analytic method which were introduced by Samoilenko. The study of such integro-differential equations leads to extend the results obtained by Butris for changing the system of non-linear integro- differential equations of Volterra type to the system of non-linear integro-differential equations of the Volterra type with boundary conditions. Theorems on a solutions are established under some necessary and

APA, Harvard, Vancouver, ISO, and other styles

3

D., Umar, and L. Bichi S. "On the Existence of Solutions of Multi-Term Fractional Order Volterra Integro-Differential Equations." International Journal of Mathematical Sciences and Optimization: Theory and Applications 10, no. 4 (2024): 99–113. https://doi.org/10.5281/zenodo.14710636.

Full text

Abstract:

In this paper, the problem of multi-term fractional order Volterra integro-differential equations is considered. The multi-term fractional order derivative part of the multi-term fractional order Volterra integro-differential equations is converted to its equivalent integral equation and Schauder’s fixed point theorem is applied to establish the existence of solutions for the multi-term fractional order Volterra integro-differential equations under some mild conditions. Furthermore, examples were given to test the applicability of the proposed theorem.

APA, Harvard, Vancouver, ISO, and other styles

4

Qahremani, E., T. Allahviranloo, S. Abbasbandy, and N. Ahmady. "A study on the fuzzy parabolic Volterra partial integro-differential equations." Journal of Intelligent & Fuzzy Systems 40, no. 1 (2021): 1639–54. http://dx.doi.org/10.3233/jifs-201125.

Full text

Abstract:

This paper is concerned with aspects of the analytical fuzzy solutions of the parabolic Volterra partial integro-differential equations under generalized Hukuhara partial differentiability and it consists of two parts. The first part of this paper deals with aspects of background knowledge in fuzzy mathematics, with emphasis on the generalized Hukuhara partial differentiability. The existence and uniqueness of the solutions of the fuzzy Volterra partial integro-differential equations by considering the type of [gH - p]-differentiability of solutions are proved in this part. The second part is

APA, Harvard, Vancouver, ISO, and other styles

5

Li, Yunfei, and Shoufu Li. "Classical Theory of Linear Multistep Methods for Volterra Functional Differential Equations." Discrete Dynamics in Nature and Society 2021 (March 11, 2021): 1–15. http://dx.doi.org/10.1155/2021/6633554.

Full text

Abstract:

Based on the linear multistep methods for ordinary differential equations (ODEs) and the canonical interpolation theory that was presented by Shoufu Li who is exactly the second author of this paper, we propose the linear multistep methods for general Volterra functional differential equations (VFDEs) and build the classical stability, consistency, and convergence theories of the methods. The methods and theories presented in this paper are applicable to nonneutral, nonstiff, and nonlinear initial value problems in ODEs, Volterra delay differential equations (VDDEs), Volterra integro-different

APA, Harvard, Vancouver, ISO, and other styles

6

Yang, Ai-Min, Yang Han, Yu-Zhu Zhang, Li-Ting Wang, Di Zhang, and Xiao-Jun Yang. "On local fractional Volterra integro-differential equations in fractal steady heat transfer." Thermal Science 20, suppl. 3 (2016): 789–93. http://dx.doi.org/10.2298/tsci16s3789y.

Full text

Abstract:

In this paper we address the inverse problems for the fractal steady heat transfer described by the local fractional linear and non-linear Volterra integro-differential equations. The Volterra integro-differential equations are presented for investigating the fractal heat-transfer.

APA, Harvard, Vancouver, ISO, and other styles

7

GIL', M. I. "POSITIVITY OF GREEN'S FUNCTIONS TO VOLTERRA INTEGRAL AND HIGHER ORDER INTEGRO-DIFFERENTIAL EQUATIONS." Analysis and Applications 07, no. 04 (2009): 405–18. http://dx.doi.org/10.1142/s0219530509001475.

Full text

Abstract:

We consider Volterra integral equations and arbitrary order integro-differential equations. We establish positivity conditions and two-sided estimates for Green's functions. These results are then applied to obtain stability and positivity conditions for equations with nonlinear causal mappings (operators) and linear integro-differential parts. Such equations include differential, difference, differential-delay, integro-differential and other traditional equations.

APA, Harvard, Vancouver, ISO, and other styles

8

Kareem, Kabiru Oyeleye, Morufu Oyedunsi Olayiwola, and Muideen Odunayo Ogunniran. "Advances In Modification of Adomian Decomposition Method and Their Application to Integral Equations." Parrot: A Multi-Disciplinary Journal of the Federal College of Education, Iwo 1, no. 1 (2024): 100–110. https://doi.org/10.5281/zenodo.15106113.

Full text

Abstract:

This study presents a new modified Adomian decomposition approach for solving Volterra-Fredholm integro-differential equations. The suggested approach attempts to improve the efficiency and accuracy of the present method for dealing with this class of equations. The modified Adomian decomposition approach was shown to be useful in generating trustworthy solutions for a wide variety of Volterra-Fredholm integro-differential equations. Our discoveries help to enhance numerical methods for solving integro-differential equations, which have applications in a variety of scientific and engineering a

APA, Harvard, Vancouver, ISO, and other styles

9

Amal M. Wadi. "Using W Transform for Solving Volterra Integro-Differential Equations." Communications on Applied Nonlinear Analysis 32, no. 7s (2025): 675–87. https://doi.org/10.52783/cana.v32.3474.

Full text

Abstract:

There are numerous uses for the Volterra integro-differential equation in the fields of mechanics, geometric probability, population dynamics, theory of rejuvenation, facts on particle size and the damping of string vibration, and transmission of heat issues. Finding the approximate or exact solutions to these equations is of interest to many mathematicians and scientists. Our aim of this paper is to explore and figure out the solution of the Volterra integro-differential equation with a convolution kernel. We now introduce the W transform for determining the solution of linear Volterra integr

APA, Harvard, Vancouver, ISO, and other styles

10

Tunç, Cemil, Fehaid Salem Alshammari та Fahir Talay Akyıldız. "On the Existence of Solutions and Ulam-Type Stability for a Nonlinear ψ-Hilfer Fractional-Order Delay Integro-Differential Equation". Fractal and Fractional 9, № 7 (2025): 409. https://doi.org/10.3390/fractalfract9070409.

Full text

Abstract:

In this work, we address a nonlinear ψ-Hilfer fractional-order Volterra integro-differential equation that incorporates n-multiple-variable time delays. Employing the ψ-Hilfer fractional derivative operator, we investigate the existence of a unique solution, as well as the Ulam–Hyers–Rassias stability, semi-Ulam–Hyers–Rassias stability, and Ulam–Hyers stability of the proposed ψ-Hilfer fractional-order Volterra integro-differential equation through the fixed-point approach. In this study, we enhance and generalize existing results in the literature on ψ-Hilfer fractional-order Volterra integro

APA, Harvard, Vancouver, ISO, and other styles

11

Journal, Baghdad Science. "Numerical Approach of Linear Volterra Integro-Differential Equations Using Generalized Spline Functions." Baghdad Science Journal 9, no. 4 (2012): 734–40. http://dx.doi.org/10.21123/bsj.9.4.734-740.

Full text

Abstract:

This paper is dealing with non-polynomial spline functions "generalized spline" to find the approximate solution of linear Volterra integro-differential equations of the second kind and extension of this work to solve system of linear Volterra integro-differential equations. The performance of generalized spline functions are illustrated in test examples

APA, Harvard, Vancouver, ISO, and other styles

12

Hasan, Nabaa N. "Numerical Approach of Linear Volterra Integro-Differential Equations Using Generalized Spline Functions." Baghdad Science Journal 9, no. 4 (2012): 734–40. http://dx.doi.org/10.21123/bsj.2012.9.4.734-740.

Full text

Abstract:

This paper is dealing with non-polynomial spline functions "generalized spline" to find the approximate solution of linear Volterra integro-differential equations of the second kind and extension of this work to solve system of linear Volterra integro-differential equations. The performance of generalized spline functions are illustrated in test examples

APA, Harvard, Vancouver, ISO, and other styles

13

Haghany, A., and Adel Kassaian. "Study of the algebra of smooth integro-differential operators with applications." Journal of Algebra and Its Applications 18, no. 01 (2019): 1950009. http://dx.doi.org/10.1142/s0219498819500099.

Full text

Abstract:

We study the algebra of integro-differential operators with smooth coefficients and kernels on a subspace of [Formula: see text]. We find a normal form for elements of this algebra and determine its unit group. The formulation of inverses gives explicit solutions of inhomogeneous linear Volterra integro-differential equations and Volterra integral equations of first kind with smooth kernels.

APA, Harvard, Vancouver, ISO, and other styles

14

Kamble Rajratna M. "Existence and Uniqueness of Continuous Solutions for Conformable Fractional Integro-Differential Equations in Cone Metric Spaces." Communications on Applied Nonlinear Analysis 32, no. 9s (2025): 1303–11. https://doi.org/10.52783/cana.v32.4138.

Full text

Abstract:

In this paper, by the application of some extensions of Banach's contraction principle in complete cone metric space, we have proved the existence and uniqueness of solutions to fractional order integro-differential equations of Volterra-Fredholm type which are defined in a cone metric space. The fractional order derivative defined in the integro-differential equation is the conformable fractional order derivative. The obtained results are used for solving a couple of fractional order integro-differential equations of Volterra-Fredholm type. Mathematics Subject Classification: 34B05.

APA, Harvard, Vancouver, ISO, and other styles

15

SURAJO LAWAN BICHI and ABUBAKAR SADIQ AHMAD. "A Hybrid of Direct Computational and Homotopy Analysis Methods for Solving Volterra-Fredholm Integro-Differential Equations." International Journal of Development Mathematics (IJDM) 1, no. 4 (2024): 026–37. https://doi.org/10.62054/ijdm/0104.03.

Full text

Abstract:

This research considered the problem of Volterra-Fredholm integro-differential equations. A method of Direct computation and Homotopy analysis for solving Volterra-Fredholm integro-differential equations (DHAMVFIDE) was proposed. Convergence analysis to the exact solution of the proposed method was estabished. Examples were solved and comparisons were made with some existing methods to get the efficiency of the proposed method.

APA, Harvard, Vancouver, ISO, and other styles

16

Lahib Ibrahim Zaidan. "Least square method for Solving Linear Fredholm and Volterra Integro – Differential Equations of the Second Kind Using Bernstein Polynomial." Journal of the College of Basic Education 18, no. 73 (2023): 121–26. http://dx.doi.org/10.35950/cbej.v18i73.9629.

Full text

Abstract:

The main purpose of this paper lies briefly in submitting least square method for solving linear Fredholm and Volterra integro differential equations of the second kind with the aid of Bernstein polynomials as basic functions to compute the approximated solutions of Fredholm and Volterra integro differential equations .Two examples are given for determining the accuracy of the proposed results method.

APA, Harvard, Vancouver, ISO, and other styles

17

Providas, Efthimios, and Ioannis Nestorios Parasidis. "A Symbolic Method for Solving a Class of Convolution-Type Volterra–Fredholm–Hammerstein Integro-Differential Equations under Nonlocal Boundary Conditions." Algorithms 16, no. 1 (2023): 36. http://dx.doi.org/10.3390/a16010036.

Full text

Abstract:

Integro-differential equations involving Volterra and Fredholm operators (VFIDEs) are used to model many phenomena in science and engineering. Nonlocal boundary conditions are more effective, and in some cases necessary, because they are more accurate measurements of the true state than classical (local) initial and boundary conditions. Closed-form solutions are always desirable, not only because they are more efficient, but also because they can be valuable benchmarks for validating approximate and numerical procedures. This paper presents a direct operator method for solving, in closed form,

APA, Harvard, Vancouver, ISO, and other styles

18

Bijura, A. M. "Singularly Perturbed Volterra Integro-differential Equations." Quaestiones Mathematicae 25, no. 2 (2002): 229–48. http://dx.doi.org/10.2989/16073600209486011.

Full text

APA, Harvard, Vancouver, ISO, and other styles

19

Chen, Yu-Bo, and Shouchuan Hu. "PBVP of volterra integro-differential equations." Applicable Analysis 22, no. 2 (1986): 133–37. http://dx.doi.org/10.1080/00036818608839611.

Full text

APA, Harvard, Vancouver, ISO, and other styles

20

Parasidis, Ioannis. "EXACT SOLUTION OF SOME LINEAR VOLTERRA INTEGRO-DIFFERENTIAL EQUATIONS." Applied Mathematics and Control Sciences, no. 1 (March 30, 2019): 7–21. http://dx.doi.org/10.15593/2499-9873/2019.1.01.

Full text

APA, Harvard, Vancouver, ISO, and other styles

21

Rautian, N. A. "Representations of the solutions for volterra integro-differential equations in hilbert spaces." Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ 517, no. 1 (2024): 85–91. http://dx.doi.org/10.31857/s2686954324030144.

Full text

Abstract:

Volterra integro-differential equations with operator coefficients in Hilbert spaces were studied. The relationship has been established between the spectra of operator functions that are the symbols of the specified integro-differential equations and the spectra of generators of semigroups. Representations of solutions for considered integro-differential equations are obtained on the basis of spectral analysis of generators of operator semigroups and corresponding operator-functions.

APA, Harvard, Vancouver, ISO, and other styles

22

Wu, Jianhong, and Huaxing Xia. "Existence of periodic solutions to integro-differential equations of neutral type via limiting equations." Mathematical Proceedings of the Cambridge Philosophical Society 112, no. 2 (1992): 403–18. http://dx.doi.org/10.1017/s0305004100071073.

Full text

Abstract:

AbstractIn this paper, we present some results on the existence of periodic solutions to Volterra integro-differential equations of neutral type. The main idea is to show the convergence of an equibounded sequence of periodic solutions of certain limiting equations which are of finite delay. This makes it possible to apply the existing Liapunov–Razumikhin technique for neutral equations with finite delay to obtain existence of periodic solutions of Volterra neutral integro-differential equations (of infinite delay). Some comparisons between our results and the existing ideas are also provided.

APA, Harvard, Vancouver, ISO, and other styles

23

Bahşı, Muhammet Mustafa, and Mehmet Çevik. "Improved Jacobi Matrix Method for Solving Multi-Functional Integro-Differential Equations with Mixed Delays." Celal Bayar Üniversitesi Fen Bilimleri Dergisi 16, no. 4 (2020): 393–401. https://doi.org/10.18466/cbayarfbe.716634.

Full text

Abstract:

In this study, we suggested a novel approach for solving multi-functional integro-differential equations with mixed delays, by using orthogonal Jacobi polynomials. These equations include various classes of differential equations, integro-differential equations and delay differential equations. This new algorithm proposes solutions for each class of these equations and combinations of equation classes, such as Volterra integro-differential equation, Fredholm integro-differential equation, pantograph-delay differential equations. Since the present method is based on fundamental matrix relations

APA, Harvard, Vancouver, ISO, and other styles

24

P, C. Jayaprakasha, and C. Shashikumar H. "Numerical Solution of Non-linear Integro-differential Equations using Operational Matrix based on the Hosoya Polynomial of a Path Graph." Indian Journal of Science and Technology 16, no. 15 (2023): 1159–67. https://doi.org/10.17485/IJST/v16i15.2353.

Full text

Abstract:

Abstract <strong>Objectives:</strong> Introduction to new numerical techniques to solve differential, difference, and integro-differential equations (IDEs) are always remaining the thrust area of research for many scientists over the centuries. The prime objective of this work is to contribute a new numerical technique to solve IDEs.<strong> Method:</strong> To address non-linear integro-differential equations, we computed an operational matrix of derivatives based on the Hosoya polynomial of the path graph in this work. <strong>Findings:</strong> Using the derived ope

APA, Harvard, Vancouver, ISO, and other styles

25

Derle, Monali, and Dinkar Patil. "Applications of The Double General Rangaig Integral Transform in Integro-Differential Equations." Indian Journal Of Science And Technology 17, no. 31 (2024): 3258–71. http://dx.doi.org/10.17485/ijst/v17i31.922.

Full text

Abstract:

Objectives : To solve integral differential equations. Method: The convolution theory and double general Rangaig integral transform was used to solve integral differential equations, precisely. Findings: The present study derives the existence condition of the double general Rangaig integral transform. Theorems proved in this study, deals with popular properties of the double general Rangaig integral transform. The double general Rangaig integral transform of Bessel's function and modified Bessel's function are calculated. The convolution theorem has been stated and demonstrated using the unit

APA, Harvard, Vancouver, ISO, and other styles

26

Khalouta, Ali. "Solution of systems of linear Caputo fractional Volterra integro-differential equations using the Khalouta integral transform method." Вестник Самарского государственного технического университета. Серия «Физико-математические науки» 29, no. 2 (2025): 207–19. https://doi.org/10.14498/vsgtu2141.

Full text

Abstract:

The Khalouta integral transform is a powerful method for solving various types of equations, including integro-differential equations and integral equations. It can also be applied to initial and boundary value problems associated with ordinary differential equations and partial differential equations with constant coefficients. The main objective of this paper is to derive solutions to systems of linear Caputo fractional Volterra integro-differential equations using the Khalouta integral transform. To solve such systems using this technique, it is essential to establish and define several key

APA, Harvard, Vancouver, ISO, and other styles

27

Burova, I. G., and Yu K. Demyanovich. "Nonlenear Integro-differential Equations and Splines of the Fifth Order of Approximation." WSEAS TRANSACTIONS ON MATHEMATICS 21 (September 23, 2022): 691–700. http://dx.doi.org/10.37394/23206.2022.21.81.

Full text

Abstract:

In this paper, we consider the solution of nonlinear Volterra–Fredholm integro-differential equation, which contains the first derivative of the function. Our method transforms the nonlinear Volterra-Fredholm integro-differential equations into a system of nonlinear algebraic equations. The method based on the application of the local polynomial splines of the fifth order of approximation is proposed. Theorems about the errors of the approximation of a function and its first derivative by these splines are given. With the help of the proposed splines, the function and the derivative are replac

APA, Harvard, Vancouver, ISO, and other styles

28

Chen, Xiaojuan, and Xiaoxiao Ma. "A Pretreatment Method of Volterra the External Boundary Value Problem of Integral Differential Equations." International Journal of Circuits, Systems and Signal Processing 15 (August 31, 2021): 1252–59. http://dx.doi.org/10.46300/9106.2021.15.136.

Full text

Abstract:

In the process of traditional methods, the error rate of external boundary value problem is always at a high level, which seriously affects the subsequent calculation and cannot meet the requirements of current Volterra products. To solve this problem, Volterra's preprocessing method for the external boundary value problem of Integro differential equations is studied in this paper. The Sinc function is used to deal with the external value problem of Volterra Integro differential equation, which reduces the error of the external value problem and reduces the error of the external value problem.

APA, Harvard, Vancouver, ISO, and other styles

29

Iyanda, Falade Kazeem, and Tiamiyu Abd`gafar Tunde. "Computatıonal Algorıthm for the Numerıcal Solutıon of Systems of Volterra Integro-Dıfferentıal Equatıons." Academic Journal of Applied Mathematical Sciences, no. 66 (June 5, 2020): 66–76. http://dx.doi.org/10.32861/ajams.66.66.76.

Full text

Abstract:

In this paper, we employ variational iterative method (VIM) to develop a suitable Algorithm for the numerical solution of systems of Volterra integro-differential equations. The formulated algorithm is used to solve first and second order linear and nonlinear system of Volterra integrodifferential equations which demonstrated a good numerical approach to overcome lengthen computational and integral simplification involves. Moreover, the comparison of the exact solution with the approximated solutions are made and approximate solutions p(x) q(t) proved to converge to the exact solutions p(x) q(

APA, Harvard, Vancouver, ISO, and other styles

30

Ibrahimov, Vagif, Galina Mehdiyeva, Mehriban Imanova, and Davron Aslonqulovich Juraev. "Application of the Bilateral Hybrid Methods to Solving Initial -Value Problems for the Volterra Integro-Differential Equations." WSEAS TRANSACTIONS ON MATHEMATICS 22 (October 20, 2023): 781–91. http://dx.doi.org/10.37394/23206.2023.22.86.

Full text

Abstract:

The many problems of natural sciences are reduced to solving integro-differential equations with variable boundaries. It is known that Vito Volterra, for the study of the memory of Earth, has constructed the integro-differential equations. As is known, there is a class of analytical and numerical methods for solving the Volterra integro-differential equation. Among them, the numerical methods are the most popular. For solving this equation Volterra himself used the quadrature methods. How known in solving the initial-value problem for the Volterra integro-differential equations, increases the

APA, Harvard, Vancouver, ISO, and other styles

31

Du, Wei-Shih, Marko Kostić, and Daniel Velinov. "Abstract Impulsive Volterra Integro-Differential Inclusions." Fractal and Fractional 7, no. 1 (2023): 73. http://dx.doi.org/10.3390/fractalfract7010073.

Full text

Abstract:

In this work, we provide several applications of (a,k)-regularized C-resolvent families to the abstract impulsive Volterra integro-differential inclusions. The resolvent operator families under our consideration are subgenerated by multivalued linear operators, which can degenerate in the time variable. The use of regularizing operator C seems to be completely new within the theory of the abstract impulsive Volterra integro-differential equations.

APA, Harvard, Vancouver, ISO, and other styles

32

Georgievskii, D. V., and N. A. Rautian. "CORRECT SOLVABILITY OF VOLTERRA INTEGRO-DIFFERENTIAL EQUATIONS ARISING IN VISCOELASTICITY THEORY." Дифференциальные уравнения 60, no. 4 (2024): 533–49. http://dx.doi.org/10.31857/s0374064124040083.

Full text

Abstract:

We discuss the issues of correct solvability and exponential stability of solutions of abstract integrodifferential equations with kernels of integral operators of general type from the space of functions integrable on the positive semiaxis. The abstract integro-differential equations are studied in this paper are operator models of viscoelasticity theory problems. The proposed approach to the study of these integro-differential equations is related to the application of the semigroups theory and can also be used to study other integro-differential equations containing integral terms of Volter

APA, Harvard, Vancouver, ISO, and other styles

33

Daliri Birjandi, M. H., J. Saberi-Nadjafi, and A. Ghorbani. "An Efficient Numerical Method for a Class of Nonlinear Volterra Integro-Differential Equations." Journal of Applied Mathematics 2018 (August 1, 2018): 1–7. http://dx.doi.org/10.1155/2018/7461058.

Full text

Abstract:

We investigate an efficient numerical method for solving a class of nonlinear Volterra integro-differential equations, which is a combination of the parametric iteration method and the spectral collocation method. The implementation of the modified method is demonstrated by solving several nonlinear Volterra integro-differential equations. The results reveal that the developed method is easy to implement and avoids the additional computational work. Furthermore, the method is a promising approximate tool to solve this class of nonlinear equations and provides us with a convenient way to contro

APA, Harvard, Vancouver, ISO, and other styles

34

Marzban, Hamid Reza, and Sayyed Mohammad Hoseini. "Solution of Nonlinear Volterra-Fredholm Integrodifferential Equations via Hybrid of Block-Pulse Functions and Lagrange Interpolating Polynomials." Advances in Numerical Analysis 2012 (December 10, 2012): 1–14. http://dx.doi.org/10.1155/2012/868279.

Full text

Abstract:

An efficient hybrid method is developed to approximate the solution of the high-order nonlinear Volterra-Fredholm integro-differential equations. The properties of hybrid functions consisting of block-pulse functions and Lagrange interpolating polynomials are first presented. These properties are then used to reduce the solution of the nonlinear Volterra-Fredholm integro-differential equations to the solution of algebraic equations whose solution is much more easier than the original one. The validity and applicability of the proposed method are demonstrated through illustrative examples. The

APA, Harvard, Vancouver, ISO, and other styles

35

Yu, Le, and Yumei Chen. "Solving Fuzzy Volterra Integro-Differential Equations By Using Fuzzy Kamal Transform." International Journal of Research in Advent Technology 10, no. 4 (2022): 1–5. http://dx.doi.org/10.32622/ijrat.104202201.

Full text

Abstract:

In this paper, the fuzzy Kamal transform is used to solve fuzzy Volterra integral-differential equations, which is based on Kamal transform. Kamal transform takes very little computation and time. Numerical examples are given to prove the effectiveness of Kamal transform in solving fuzzy Volterra integro-differential equations

APA, Harvard, Vancouver, ISO, and other styles

36

Oja, Peeter, and Mare Tarang. "Stability of the spline collocation method for Volterra integro-differential equations." Acta et Commentationes Universitatis Tartuensis de Mathematica 6 (December 31, 2002): 37–49. http://dx.doi.org/10.12697/acutm.2002.06.05.

Full text

Abstract:

Numerical stability of the spline collocation method for Volterra integro-differential equations is investigated and the connection between this theory and the corresponding theory for Volterra integral equations is explored. A series of numerical tests is presented.

APA, Harvard, Vancouver, ISO, and other styles

37

Mohammed Khalid Shahoodh. "Using Touchard Polynomials Method for Solving Volterra-Fredholm Integro-Differential Equations." Tikrit Journal of Pure Science 26, no. 5 (2021): 92–96. http://dx.doi.org/10.25130/tjps.v26i5.184.

Full text

Abstract:

The goal of this paper is to introduce numerical solution for Volterra-Fredholm integro-differential equations of the second kind. The proposed method is Touchard polynomials method, and this technique transforms the integro-differential equations to the system of algebraic equations. Four examples are presented in order to illustrate the accuracy and efficiency of this method

APA, Harvard, Vancouver, ISO, and other styles

38

Bhaskar, A. Mundewadi*1 &. Ravikiran A. Mundewadi2. "COSINE AND SINE (CAS) WAVELET COLLOCATION METHOD FOR THE NUMERICAL SOLUTION OF INTEGRAL AND INTEGRO-DIFFERENTIAL EQUATIONS." INTERNATIONAL JOURNAL OF ENGINEERING SCIENCES & RESEARCH TECHNOLOGY 7, no. 1 (2018): 455–68. https://doi.org/10.5281/zenodo.1147622.

Full text

Abstract:

Cosine and Sine (CAS) wavelet collocation method for the numerical solution of Volterra, Fredholm integral and integro-differential equations, mixed Volterra-Fredholm integral equations. The method is based Cosine and Sine (CAS) wavelet approximations. The Cosine and Sine (CAS) wavelet is first presented and the resulting Cosine and sine wavelet matrices are utilized to reduce the integral and integro-differential equations into a system of algebraic equations, which is the required Cosine and Sine (CAS) coefficients, are computed using Matlab. The technique is tested on some numerical example

APA, Harvard, Vancouver, ISO, and other styles

39

Rautian, N. A. "Semigroups Generated by Volterra Integro-Differential Equations." Differential Equations 56, no. 9 (2020): 1193–211. http://dx.doi.org/10.1134/s0012266120090098.

Full text

APA, Harvard, Vancouver, ISO, and other styles

40

Nguyen, Tien Dung. "LINEAR MULTIFRACTIONAL STOCHASTIC VOLTERRA INTEGRO-DIFFERENTIAL EQUATIONS." Taiwanese Journal of Mathematics 17, no. 1 (2013): 333–50. http://dx.doi.org/10.11650/tjm.17.2013.1728.

Full text

APA, Harvard, Vancouver, ISO, and other styles

41

Georgiev, Svetlin G. "Volterra Integro-Differential Equations on Time Scales." International Journal of Applied and Computational Mathematics 3, no. 3 (2016): 1577–87. http://dx.doi.org/10.1007/s40819-016-0207-2.

Full text

APA, Harvard, Vancouver, ISO, and other styles

42

Rashidinia, Jalil, and Ali Tahmasebi. "Systems of nonlinear Volterra integro-differential equations." Numerical Algorithms 59, no. 2 (2011): 197–212. http://dx.doi.org/10.1007/s11075-011-9484-3.

Full text

APA, Harvard, Vancouver, ISO, and other styles

43

Gripenberg, Gustaf. "Volterra integro-differential equations with accretive nonlinearity." Journal of Differential Equations 60, no. 1 (1985): 57–79. http://dx.doi.org/10.1016/0022-0396(85)90120-2.

Full text

APA, Harvard, Vancouver, ISO, and other styles

44

Tunç, C., and S. A. Mohammed. "On asymptotically stability, uniformly stability and boundedness of solutions of nonlinear Volterra integro-differential equations." Ukrains’kyi Matematychnyi Zhurnal 72, no. 12 (2020): 1708–20. http://dx.doi.org/10.37863/umzh.v72i12.6037.

Full text

Abstract:

UDC 517.9 In this paper, two new Lyapunov functionals are defined. We apply these functionals to get sufficient conditions guaranteeing the asymptotic stability, uniform stability, and boundedness of solutions of certain nonlinear Volterra integro-differential equations of the first order. The results obtained are improvements and extensions of known results that can be found in literature. We also suggest examples to show the applicability of our results and for the sake of illustrations. Using MATLAB-Simulink, in particular cases we clearly show the behavior of orbits of Volterra integro-dif

APA, Harvard, Vancouver, ISO, and other styles

45

Zhu, Jiang, Yajuan Yu, and Vasile Postolica. "Initial value problems for first order impulsive integro-differential equations of Volterra type in Banach spaces." Journal of Function Spaces and Applications 5, no. 1 (2007): 9–26. http://dx.doi.org/10.1155/2007/968435.

Full text

Abstract:

In this paper, we use a new method and combining the partial ordering method to study the existence of the solutions for the first order nonlinear impulsive integro-differential equations of Volterra type on finite interval in Banach spaces and for the first order nonlinear impulsive integro-differential equations of Volterra type on infinite interval with infinite number impulsive times in Banach spaces. By introducing an interim space and using progressive estimation method, some restrictive conditions on impulsive terms, used before, such as, prior estimation, noncompactness measure estimat

APA, Harvard, Vancouver, ISO, and other styles

46

Shior, M. M., T. Aboiyar, S. O. Adee, and E. C. Madubueze. "A Collocation Method Based on Euler and Bernoulli Polynomials for the Solution of Volterra Integro-Differential Equations." Nig Annals of Pure & Appl Sci 5, no. 1 (2022): 281–88. https://doi.org/10.5281/zenodo.7142991.

Full text

Abstract:

<strong>ABSTRACT</strong> In this research, we constructed collocation methods for approximating the solutions of Volterra integro-differential equations using Bernoulli polynomials and Euler polynomials as basic functions. Sample problems ranging from linear first to second order Volterra integro-differential (VIDEs) equations using the methods developed were solved.  The method was implemented using MAPLE 17 and MATLAB software and the obtained results are compared with the exact solution for the polynomials. Results revealed that Bernoulli Polynomials has the best accuracy for the firs

APA, Harvard, Vancouver, ISO, and other styles

47

Andre, Traore, Bationo Jeremie Yiyureboula, and Francis Bassono. "Application of a New Approach to the Adomian Method to the Solution of Fractional-order Integro-differential Equations." Journal of Advances in Mathematics and Computer Science 40, no. 5 (2025): 28–47. https://doi.org/10.9734/jamcs/2025/v40i51996.

Full text

Abstract:

In this paper we solve fractional order integro-differential equations of Fredholm type and Volterra type. For the solution we use a new Adomian decompositional method.In the first part we give the basic notions on fractional operators, essential to our work. The second part is devoted to the description and convergence of the method. In the third part, the method has been used to solve fractional order integro-differential equations of Fredholm type and Volterra type. The last part is devoted to the conclusion and some bibliographical references.

APA, Harvard, Vancouver, ISO, and other styles

48

Bakke, Vernon L., and Zdzisław Jackiewicz. "Stability analysis of reducible quadrature methods for Volterra integro-differential equations." Applications of Mathematics 32, no. 1 (1987): 37–48. http://dx.doi.org/10.21136/am.1987.104234.

Full text

APA, Harvard, Vancouver, ISO, and other styles

49

Andreev, A. S., and O. A. Peregudova. "On the Stability and Stabilization Problems of Volterra Integro-Differential Equations." Nelineinaya Dinamika 14, no. 3 (2018): 387–407. http://dx.doi.org/10.20537/nd180309.

Full text

APA, Harvard, Vancouver, ISO, and other styles

50

Khaireddine, Fernane. "Numerical solution of the general Volterra nth-order integro-differential equations via variational iteration method." Asian-European Journal of Mathematics 13, no. 02 (2018): 2050042. http://dx.doi.org/10.1142/s1793557120500424.

Full text

Abstract:

In this paper, we use the variational iteration method (VIM) to construct approximate solutions for the general [Formula: see text]th-order integro-differential equations. We show that his method can be effectively and easily used to solve some classes of linear and nonlinear Volterra integro-differential equations. Finally, some numerical examples with exact solutions are given.

APA, Harvard, Vancouver, ISO, and other styles

We offer discounts on all premium plans for authors whose works are included in thematic literature selections. Contact us to get a unique promo code!